NBER WORKING PAPER SERIES
INNOVATION AND WELFARE:
RESULTS FROM JOINT ESTIMATION OF PRODUCTION AND DEMAND FUNCTIONS
Jordi Jaumandreu
Jacques Mairesse
Working Paper 16221
http://www.nber.org/papers/w16221
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
July 2010
Previous versions of this paper have also circulated under the title "Using price and demand information
to identify production functions". The authors gratefully acknowledge useful comments by D. Ackeberg,
D. Coe, U. Doraszelski, C. Lelarge, A.Pakes and seminar audiences at CNRS-OFCE Workshop on
Innovation, Competition and Productivity (Nice, December 2005), BDF Seminar on Innovation (Enghien-les-Bains,
July 2007), AEA meetings (New Orleans, January 2008), TEMA seminar (Paris, January 2008), NBER
productivity seminar (Cambridge, March 2008), HECER workshop on innovation (Helsinki, August
2008). The views expressed herein are those of the authors and do not necessarily reflect the views
of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2010 by Jordi Jaumandreu and Jacques Mairesse. All rights reserved. Short sections of text, not
to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including
© notice, is given to the source.
Innovation and Welfare: Results from Joint Estimation of Production and Demand Functions
Jordi Jaumandreu and Jacques Mairesse
NBER Working Paper No. 16221
July 2010
JEL No. C33,D21,D24,D62,O31
ABSTRACT
This paper develops a simple framework to estimate the parameters of the production function together
with the elasticity of the demand for the output and the impact of demand and cost shifters. The use
of this framework helps, in the first place, to treat successfully the difficult problem of the endogeneity
of input quantities. But it also provides a natural way to assess the welfare effects of firms’ innovative
actions by estimating their impact on both cost and demand. We show that the total current period
(static) welfare gains of introducing a process or a product innovation are, on average, about 1.6%
and 4%, respectively, of the value of the firm’s current sales. The increase in consumer surplus amounts
to two- thirds of these gains in the first case and half in the second.
Jordi Jaumandreu
Department of Economics
Boston University
270 Bay State Road
MA 02215, Boston
USA.
jordij@bu.edu
Jacques Mairesse
CREST-INSEE
15, Boulevard Gabriel PERI
92245 MALAKOFF CEDEX
FRANCE
and NBER
mairesse@ensae.fr
1.Introduction
This paper develops a simple framework to estimate the parameters of the production
function together with the elasticity of the demand for the output and the impact of demand and cost shifters.The estimation of cost and demand parameters together with the
production function serves two purposes. Firstly, it helps to deal succesfully with one of
the most difficult problems in estimating production functions, the endogeneity of the input
quantities. Secondly, it provides a natural framework to assess the effects of firms’ innovative actions by estimating their impact on both cost and demand. The framework needs
information on prices, innovation data, and other demand shifters, but it nicely illustrates
how much can be gained by having this information. We show that the total current period
(static) welfare gains of introducing a process or a product innovation are, on average, about
1.6% and 4%, respectively, of the value of the firm’s current sales. Increase of consumer
surplus amounts to two-thirds of the effect in the first case and half in the second.
Estimation of microeconomic production functions has proved to be a hard task because
of the simultaneous determination of output and relevant inputs by the same partially unobserved forces. Both chosen input quantities and produced ouput are partially determined
by the unobservable productivity level which characterises the firm-specific production function and that is likely to evolve over time endogenously and in complex ways.1 Firms engage
in R&D expenditures and introduce process and product innovations with the aim of enhancing productivity, and the results are partly random because these activities and their
results are subject to uncertainty. The problem of simultaneous determination of inputs and
output, as well as the relevance of the simultaneous equations framework for dealing with
this setting, was first stressed by Marschak and Andrews (1944). Griliches and Mairesse
(1998), and more recently, Ackerberg, Benkard, Berry and Pakes (2005), have surveyed the
efforts to develop estimation methods which are robust to the simultaneity biases.
Two methods have dominated the most recent approaches. One stresses the equation
1
This unobservability may also eventually create a selectivity problem because firms with the worst
productivity performance may be induced to leave the market.
2
transformations under which the unobserved productivity levels of the production relationship are likely to be differenced out, or at least reduced to limited forms of residual
correlation. Then it proposes the use of suitable lags of the variables as instruments (IV)
orthogonal to the remaining disturbances to obtain identification. Panel “fixed effects” assumptions about productivity and the estimation of equations in first differences belong to
this tradition. Blundell and Bond (2000), for example, present a sophisticated variety of
this strategy which allows for an unobserved composite term consisting of a "fixed effect,"
an autoregresive component and an uncorrelated disturbance, and derive the right moments
to be employed in this context.
2
The alternative approach proposes semiparametric methods to control for (Markovian)
correlated productivity terms, based on the observability of the investment (or, more in
general, input choice) decisions of the firms. Optimal input decisions convey information
about the level of productivity, and if the corresponding demands can be inverted, they
can be used to replace the unobserved term. With unobserved productivity adequately
controlled for, correlation of input quantities ceases to be a problem. Olley and Pakes
(1996) first proposed this method, which has also been developed by Levinsohn and Petrin
(2002) and Ackerberg, Caves and Frazer (2007) and applied by many others. Doraszelski and
Jaumandreu (2007) extend the method to consider unobserved productivity which evolves
under the influence of R&D investments, i.e., endogenously.
Against this background, this paper aims to explore the use of information on the firmlevel prices and shifters to identify the parameters of the production function. It takes
seriously the often quoted reference of Griliches that addressing the simultaneity problem
is harder “without constructing a complete production and input decision behavior model.”
We draw on the idea first discussed in Griliches and Mairesse (1984) about how to deal
with the simulaneity-induced problems by using semi-reduced forms of the relevant eco2
Given the difficulties with this type of estimator, they argue that standard panel first-difference GMM
estimates are likely to present large finite-sample biases due to the time series persistence properties of some
of the variables involved. They propose exploiting additional instruments in an extended GMM estimator
which includes level moments.
3
nomic system. The framework is very simple: by specifying the system of equations which
determines output and (variable) inputs, one includes enough exogenous variables to solve
and express every endogenous variable in terms of its exogenous determinants. Then a
straightforward LS estimator can be applied with much weaker assumptions about the evolution of the unobservables, and the structural parameters can be recovered by one of the
usual methods.
Following Griliches and Mairesse (1984), we enlarge the model by considering that firms
compete in an imperfectly competitive environment, experiencing a downward-sloping demand for their products, and that price must therefore be taken as an additional endogenous
variable simultaneously set by the firm.3 Hence we consider that the suitable system of
equations includes the production function, the (dual) cost function and the derived input
demand relationships, the demand for the firm product and the pricing rule. In this setting,
we show that both the production function and the cost equation can be rewritten in terms
of exogenous determinants in addition to the fixed factors (semi-reduced form) and used
to estimate the relevant parameters. We should remark, however, that we will find some
need for partly instrumenting the input prices as we use observed prices that are only rough
measures of the relevant shadow prices.4 We also derive an alternative semi-reduced form
consisting of the equation for output and specifying the other as an equation for price. This
specification adds a little complexity as the new equation must explain possible changes in
margins in addition to costs.
We hence enlarge the system employed in Griliches and Mairesse (1984) by adding a
firm-specific demand relationship, which we specify depending on unobserved demand ad3
If firms were perfectly competitive, the production function (with short-run decreasing returns to scale)
combined with equations of demand for variable inputs, depending on output quantity and output and input
prices, would be all that is needed to obtain a set of semi-reduced form equations. When firms must be
taken as having some market power, price becomes an endogenous variable set with a markup on marginal
cost (which through duality inherits all unobserved efficiency that production function may have) according
to the state of competition.
4
Shadow prices are the consequence of input adjustment costs. For recents discussions on these costs,
see, for example, Delgado, Jaumandreu and Martin-Marcos (1999) and Bond and Soderbom (2005).
4
vantages and observed demand shifters and price, as well as a firm pricing rule. Imperfect
competition therefore gives rise to a more complex system, but also gives a natural and theoretically sound role for the use of demand shifters in the identification of the production
function. In addition, the method has the important advantage that it does not rely on
specific distributional assumptions about productivity and other unobservables. The main
requirement is, however, firm-specific information good enough to estimate the resulting
system.
Demand is, however, much more than a device to help to estimate the parameters of
the production function consistently. It adds the piece which is just needed to assess the
welfare effects of the innovative actions of the firms. The production function and its dual,
the cost function, estimate at most the cost effects of innovation. Process innovation, aimed
at reducing production costs, will show that its effect is to increase productivity and reduce
costs. Product innovation, aimed at enlarging demand, will not show any effect if it has no
cost or a small amount of cost consequences. The demand relationship adds the possibility
of asssessing the impact of product innovation and, more generally, the profitability of
any type of innovation and its associated consumer surplus effects. The profitability of a
cost-reducing innovation is only measurable if one can estimate how it is translated into a
demand enlargement. The profitability of a product innovation is to be assessed just by the
amount of this enlargement, and demand is the instrument needed to assess the increases
in consumer surplus associated with both demand enlargements.
By adding the estimation of demand parameters, we hence add the possibility of computing the private and social returns of innovation.5 In addition, this renders it possible to
compare them to their observed costs in the form of R&D expenditures. This has a potential
of applications that we plan to illustrate. Firstly, by comparing profits and costs, one can
derive the degree of current incentives, the anatomy of costs, especially the presence and
size of sunk costs, and the likely presence and size of "market failures" (socially profitable
innovations subject to zero or negative private profitabilities). Secondly, by measuring how
5
Measuring welfare gains from innovation, particularly product innovation, is a hot topic which begins
with Trajtemberg (1993) and Hausman (1997).
5
firms discount static profits over time, one can learn about the uncertainties of innovation
expenditures and the intensity of competition. We want to address some of these points in
future versions of this paper, in which we also plan to allow for more heterogeneous firm
demands.
Using a rich data set consisting of (unbalanced) observations on almost 1,000 Spanish
manufacturing firms during the period 1990-1999, we present production function parameter estimates along an estimate for the elasticity of demand and the impact of cost and
demand shifters. We apply the estimator to relatively small samples for 6 industries, which
allows us to take into account the heterogeneity in production as well as check the feasibility
and robustness of our estimator. Information on firms includes firm-level variations for the
price of the output and the price of the inputs, the introduction of technological (process
and product) innovations and additional demand shifters. We estimate the structural parameters from the semi-reduced forms using non-linear GMM methods, but we report and
discuss in appendices some estimates obtained with conventional OLS and IV estimators.
The rest of the paper is organised as follows. Section 2 explains the theoretical framework and derives the semi-reduced forms. Section 3 explains the data and presents the
econometric specification and method of estimation. Section 4 presents the main estimates
and Section 5 concludes. One data appendix provides some detail on the sample, the employed variables and descriptive statistics and another gives information on some previous
estimates.
2. A semi-reduced form system
2.1 Production and demand
Assume that firms have production functions of the form  =  (1   ) exp(1 ), where
 represents output, 1 is a vector of productivity (and hence cost) shifters,  stands for
a vector of fixed inputs,  for variable inputs and exp( 1 ) represents the firm-idiosycratic
productivity level reached by the firm (we drop firm and time subindices for simplicity
and we adopt a quite common notation to express productivity). Assume at the same
6
time that the production function is (perhaps locally) homogeneous to degree  in the
variable inputs; i.e.,  is the sum of the elasticities of these inputs. The terms exp( 1 ) are
observed by the firm, but not for the econometrician, and evolve over time in an unspecified
manner. The most usually considered productivity shifter is process innovation. Note
that the production function assumptions imply a dual cost function of the form  =
 ∗ (1   )( exp(1 ))1 , where  stands for the vector on variable input prices. Firms
are going to choose  and  simultaneously and we assume, without loss of generality, that
firms choose  in order to minimize costs given exp( 1 )In what follows, we explain how
firms determine .
Assume that there is some product differentiation among the firms which compete in a
given market. Demand for a firm’s product is given by a firm-specific demand function of
the form  = (2   ) exp( 2 ), where 2 is a vector of demand shifters and  is the price
set by the firm. Idiosyncratic demand terms exp(2 ) reflect persistent demand advantages
and firm-specific demand shocks, both observed only by the firm. To simplify notation, we
assume the prices of rivals included among the shifters.6 Other demand shifters may be
either exogenously driven (e.g., the state of the market) or reflect firm investments (e.g.,
advertising and product innovation).
The elasticity of demand with respect to  must be understood as the structural elasticity,
which mainly reflects the degree of product differentiation. In fully competitive situations,
it may tend to (minus) infinity. We assume  is the result of firms pricing according to the
rule  = (1 + ) 0 , where  0 stands for (short-run) marginal cost and  is the markup
which results from the particular behavior of firms. Notice that we keep ourselves impartial
to the particular games that firms play by specifying a general markup  which may be
consistent with different equilibria. We will only care about possible changes of  over
time, not about their level.
Assume that firms set prices given the state of demand and then variable input quantities
are chosen (at competitive prices, but possibly subject to adjustment costs) according to the
6
In practice, rivals’ prices are not observable and we will assume that their effect is picked up by the time
dummies.
7
output to be produced and the level reached by productivity. Input quantities are therefore
endogenous in the production function relationship (i.e., they are correlated with the unobserved term exp( 1 )). However, consideration of the way the firm sets price according to
demand, and hence also decides output, brings in a natural set of structural exogenous or
predetermined determinants for output and inputs. They can be used, together with input
prices and other cost shifters, to write reduced form equations for output and cost. This is
shown in what follows.
We are going to set our model in terms of growth rates, log-differencing the involved
equations. This has at least two advantages. Firstly, we can then use in the analysis
some variables which are available only in terms of growth (e.g., price growth rates, which
correspond to price indices whose levels are meaningless). Secondly, we can deal more safely
with a high degree of heterogeneity. Unobservable firm-specific, time-invariant effects are
differenced out; we do not need to specify markup levels, and equations in terms of growth
rates may be thought of as approximating general functional forms. On the other hand,
our exercise supports the idea that a suitable econometric specification in first differences
plus high quality data produce satisfactory results
7
2.2 Differencing the equations
Assuming that there are  and  fixed and variable factors respectively, log-differencing
the production function gives8
7
An important problem has been attributed to the employment of differences in the context of highly
persistent data (see, for example, Blundell and Bond, 2000) : the lack of correlation between current growth
rates and past levels of the variables may seriously bias IV estimators. But this lack of correlation can be
seen just as a third advantage in our context. As we are going to use only rates of change of exogenous and
predetermined variables as regressors, we can expect no correlation between regressors and errors, even with
serially correlated residuals.
8
A disturbance term, uncorrelated with the included variables, can be added meaningfully to each of the
relationships that we discuss in what follows without any substantial change in the results. We avoid doing
this only for simplicity of notation.
8
 = 1 +
P
  +

P
  + ∆ 1
(1)

where small letters stand for growth rates. Writing  for the rate of growth of average
variable-cost ( =
()
 ),
we can obtain the log-differenced average cost function which
follows
 = −1 −
∆ 1
1P
1P
1
  +
  + ( − 1) −
 
 


(2)

First-order conditions of cost minimisation for each variable input are given by  0 
=

 , which can be manipulated to obtain the cost-share/input-elasticities equality

,
 
()
=
which give the relationships
 =  − ( − )
(3)
Endogeneity of  in equation [1] must be understood as the effect of its determination
through the  and  values, which contain  1 .
Log-differentiation of demand gives the relationship
 = 2 −  + ∆2
(4)
where  stands for the elasticity of demand with respect to the product price. And, at the
same time, the log differences of the pricing rule can be written as
 = ∆ + 
(5)
where ∆ stands for the markup changes.
Let us briefly discuss the nature of the terms ∆1 and ∆2 before using these equations.
Even if  1 and  2 are time persistent, their differences can range from serially uncorrelated
disturbances to fully autocorrelated errors depending on the specific assumptions one is
willing to make.9 Fortunately, we are not obliged to make a choice. We simply assume that
9
According to the current assumptions in the specification of production functions, the term ∆1 can be:
9
∆1 ≡ 1 is a distributionally unspecified disturbance potentially correlated with current
and possibly past input choices and that the same goes for ∆ 2 ≡ 2 .
2.3 Reduced form
Now we are ready to use the system of equations (1)-(5) to obtain reduced forms for  and
, respectively. Using (5) and (4) to express  in terms of , the demand shifters and margin
changes. Then, replace the  which appears in [2] with this expression. Input changes can
be written as  = (1 − 1 )  −  +
 =  1 1 +
where  1 = 1 ,   =

,
 =
P


,
2

− ∆ +
   −
2 =

 ,
P

2
 .
It follows that
   +  2 2 −   ∆ + 1
 =


(6)

,  = 1 − (1 − 1 ), and 1 = 1 1 + 
2 .
Similarly,  can be replaced in (4) using equation (5). Then we have output changes
in terms of demand shifters, margin changes and ; that is,  = 2 − ∆ −  + 2 .
Substituting this for  in equation (3), we obtain
 = − 1 1 −
where  1 =
1
 ,
 =

 ,
 =
P

 ,
   +

2 =
P

1−
 ,
   +  2 2 −   ∆ + 2
 =
1−

1
and 2 = − 
1 +
(7)
1−
 2 .
To implement the system, the effects represented by 1  2 and ∆ must of course be
measured by specific indicators. But, in principle, all explanatory variables in equations
(6) and (7) can be considered, under appropriate assumptions, to be either exogenous (
at least when observed prices are enough, and shifters exogenous) or predetermined ( and
a) a serially uncorrelated disturbance, because 1 is a random walk (i.e., 1 = 1−1 +1 with 1 ∼ (0),
an uncorrelated residual); b) a disturbance presenting a limited serial correlation, because  1 has two
components, a “fixed” component which remains unchanged over time and a time- varying uncorrelated shock
(e.g.,  1 = 1 + 1 with 1 ∼ (0) and hence ∆1 = (1 − 1−1 ) ∼ (1)); c) a serially correlated
disturbance because 1 follows an (1) (i.e., 1 = 1−1 +1 and hence 1 −1−1 = −(1−)−1 +1 )
or a combination of this and an (0) disturbance; see, e.g., Blundell and Bond (2000); d) a serially
correlated disturbance because 1 follows an unspecified Markov process (i.e., 1 = (1−1 ) + 1 and
hence 1 − 1−1 = (−1 ) − (−2 ) + 1 − 1−2 ); see, e.g., Olley and Pakes (1996).
10
perhaps some endogenous shifters). Disturbances 1 and 2 are presumably correlated, and
their structure depends on the properties of 1 and  2 . The relationships involved allow for
the identification of the production function and demand parameters.10 The structure of
the elasticities is identified in each equation, but total short and long-run elasticities can
only be identified using both equations to obtain .
Alternatively, the second equation can be set in terms of price. Using (4) to replace  in
(2) and plugging the result in (5) gives the following equation
 = − 1 1 −
where  1 =
1
 ,
 =

 ,
 =
P


 ,
   +
2 =
P

1−
 ,
   +  2 2 +   ∆ + 20
 =


and 20 =
(8)
1−
 2 .
The system in terms of price may in principle separately identify the effects of one particular variable if this variable is having an effect as a demand shifter and another as a
markup shifter. For this reason, and in particular for testing the presence of such effects,
this equation may play a useful role (see below).
2.4 Testing
The previous framework allows for testing the specification of the effects quite easily.
Suppose firstly that there is a demand shifter that is also a potential shifter of productivity
(or vice-versa). For example, let’s say that we want to know if product innovations have a
productivity effect (i.e., they should be included in the production function in addition to
their role as a shifter of the demand function). Let the corresponding indicator be called 
  6= 0 and  6= 0 in the
and let the effects be specified as 1 =    and 2 = 
  If 


Parameters of the two equations are subject to the following relationships:  = 11 =  =   22 =
P


 



P
P   =
P
,  =
or, in terms of the 
1− ,   = 1− and  = +(−1)

+(−1)

+(−1)

P


 
 P
P   =
P
and  =
 Long run elasticity of scale is
parameters,  =
1+(−1)

1+(−1)

1+(−1)

P
P
 +  .
10
11
output and cost equations we have total effects
  
(  + 
 )
  
1 
1−
(−
 + 
 )

1− 
1 

  + 
 =

 
1
1− 
  =
−    +

 
and 0 :   = 0 can be tested simply as the equality of the elasticity coefficients on
variable  in both equations.
Suppose now that we have doubts about the possible effect of variable  on the markup
(suppose, for example, that the question is whether product innovation changes margins in


addition to shifting demand). Specify the effects as 2 = 
  and ∆ =   If  6= 0
and 
 6= 0 in the output and price equations we have total effects
 
 −
 
1− 
 +
 
 
  =
 
 
  =
 
 
( − 
 )
 
1− 
 
( −
 )

1− 
and 0 : 
 = 0 can be tested simply as the equality of the elasticity coefficients on variable
 in both equations. It is easy to check that, in this case, the test cannot be performed in
the ouput and cost equations (both elasticities are equal, conveying the same mix of the
two effects).
3. Data and econometric specification
3.1 Data
We present estimates based on six (unbalanced) industry samples, which amount to a
total of nearly 1,000 Spanish manufacturing firms, observed during the period 1990-1999.
All variables come from the survey ESEE (Encuesta Sobre Estrategias Empresariales), a
firm-level panel survey of Spanish manufacturing starting in 1990. At the beginning of
this survey, firms with fewer than 200 workers were sampled randomly by industry and
size strata, retaining 5%, while firms with more than 200 workers were all requested to
12
participate, and the positive answers represented more or less a self-selected 60%. To
preserve representation, samples of newly created firms were added to the initial sample
every subsequent year. At the same time, there are exits from the sample, coming from both
death and attrition. The survey then provides a random sample of Spanish manufacturing
with the largest firms oversampled. A Data Appendix provides details on the variables
definition, sample composition, industry breakdown and reports some descriptive statistics.
Information on the firms include, in addition to the usual output and input quantity
measures, the firm-level variations for the price of the output and the price of the inputs,
the introduction of technological (process and product) innovations, and some demand
shifters. Let us detail the variables. Firstly, we have the more usual variables: output
(deflated production), an estimate of capital stock, labor measured in total (effective) hours
of work, intermediate consumption (also deflated) and the firm’s self reported utilisation
of the standard capacity of production. In addition, we compute variable cost as the sum
of the wage bill and intermediate consumption, and estimate the hourly wage by dividing
the wage bill by total hours of work. But we also have some less usual firm-level variables
which play a key role in our estimations. Firstly, we have the yearly (average) output price
change as reported by the firm. Secondly, firms also provide an (average) estimate of the
change in the cost of inputs grouped in three sets: energy, materials and services, which
are combined in a price index for materials. Finally, we can compute a firm specific user
cost of capital using the interest rate paid by the long-term debt of the firm plus the rough
estimate of a 0.15 depreciation rate and minus the consumer prices index variation. In
addition, we are going to use the following shifters: a dummy representing the introduction
of process innovations, a dummy reporting the introduction of product innovations, the rate
of increase of firm advertising, and an index of the dynamism of the firm’s specific market.
As we have no observations on rivals’ prices , we will let the time dummies pick up their
effect.
From the start, we are going to assume some constraints on the specification of the shifters.
We take the introduction of process innovations as a cost (and only cost) shifter. At the same
time, we will assume that there are three demand shifters: product innovations, advertising
13
and market dynamism. Let us suppose for the moment that there are no margin changes,
although it seems pretty clear that all these demand shifters can also induce changes in
margins.
3.2 Specification and indentification conditions
Our specification of the reduced form for output (6) will include: the fixed input capital
 the prices of variable inputs (wage, , and materials,  ), and the shifters. Let us
denote  for the introduction of innovations (with  for process and  for product),  for
market dynamism and  for the growth rate of advertising. After some experimenting, we
decided to enter utilisation of capacity  restraint to have the same coefficient as capital.
Our specification for the reduced form for cost (7) will include the same variables, although
affected by different theoretically constrained coefficients. A set of time dummies is included
in each equation, with no cross restrictions but coefficients constrained to add up to zero
in each equation. Hence the system is
 =  0 +    +   ( + ) +    +    +    +    +    +  + 1
 =  0 +    +   ( + ) +    +    +    +    +    +  + 2




i  =
i
,   = − h
,  = − h

1−(1− 1 )( + )
1−(1− 1 )( + )
 1−(1− 1 )( + )
 1−(1− 1 )( + )




i
h
i
− 1−(1− 1)(
,  = h
 = − 1−(1− 1 )( + )    =
 + )
 1−(1− 1 )( + )
 1−(1− 1 )( + )


where   =
 =
and   =

h
i,
 1−(1− 1 )( + )
 =
(1−)
h
i
 1−(1− 1 )( + )
for  =   
So we have a two-equation model with nonlinear cross-restrictions in the parameters
which can identify production elasticities, returns to scale and demand elasticity as well as
the impact of the shifters. In what follows, let us briefly discuss the identification conditions
of the specification.
Firstly, under competitive factor markets and no measurement problems, we can expect
the input prices to be orthogonal to both equation errors, i.e., () = 0 and ( ) = 0
Secondly, we can assume that the cost and demand shifters are orthogonal to the primitive
14
 errors of the production function and demand equations, and hence also orthogonal to
both equation errors. This doesn’t need much discussion for the case of the indicator of
market dynamism, which repesents the exogenous market conditions in which the firm
is involved. It seems quite sensible also for the dummies representing the introduction
of innovations. Even if the introduction of innovations can perhaps be related to past
unobserved firm-level productivity (for example, through investment in R&D), it is more
difficult to think of reasons why this relation should carry over the contemporaneous change
in the level of productivity. And the same can be said for the rate of change in advertising
expenditures, although here perhaps it could be argued that some advertising can be aimed
at counterbalancing expected adverse demand shocks inducing some correlation. Thirdly,
both equations include the predetermined input capital that, with 1 and 2 autocorrelated
and presumably inducing autocorrelation in 1 and 2 , cannot be considered exogenous.
That is, we expect () 6= 0 and some instrument must be used at least for this variable.
We are going to use the price condition that presumably determines the level of investment
in the long run: the user cost of capital .
Although dicussion points to the necessity of only one instrument, in practice, preliminary
estimates quickly showed that some instrumenting of the input prices was needed to obtain
sensible coefficients. The likely reason is the errors that observed prices include with respect
to prices relevant to the firm maximization problem. Even setting aside pure measurement
problems, the costs of adjustment of the inputs make unobserved "shadow" prices relevant,
at least for replacing quantities. This only affects the first equation. We try to solve the
need to predict the right "shadow" prices for wages and the price of materials in the first
equation by using the effective hours per worker () and a variable representing marketwide price decreases (, which we assume are correlated to materials price changes). So,
our basic instrument sets can be written as 1 = {1           } and
2 = {1            } In practice, we use two versions of the user cost
instrument: the user cost of capital for the firm itself and the user cost of capital for the
rivals, computed using data on the rest of the firms in the same industry. We also use the
square of both variables as instruments.
15
3.3 Econometric method
The model fits most naturally in the non-linear two-equation GMM problem
⎡
⎤0 ⎡
⎤
1 P
1 P
0 
0 


1
1
 1
⎦  ⎣   1
⎦
min ⎣  P
1
1 P

0
0 



 2 2
 2 2


where  is  ×   with  = 1 2 and  = 1 and which can be implemented using a
first-step weighting matrix
⎡
=⎣
( 1
P
0
−1
 1 1 )
0
( 1
0
P
0
−1
 2 2 )
⎤
⎦
A robust variance estimate of the parameters can then be obtained by employing the
( 0  )
formula  () = (Γ0 Γ)−1 Γ0 (0  0  )Γ(Γ0 Γ)−1 , where Γ = (   ) is estimable
P ( 0 b )
P
using 1    and (0  0  ) by using 1  0 b b0  In practice, the equations can be
"concetrated out" for the estimation of parameters which enter linearly and the non-linear
search is only over        and      and  
4. Estimation results
Table 1 presents the results of the joint estimation by industries of the production and cost
functions (The appendix reports some previous experiments with simpler estimators using
the whole sample). The result, from the point of view of production function parameter
estimation, is very good. The elasticities of capital, labor and material are sensible and
estimated with precision. Returns to scale are not far from unity, with the only exception
sector 10. Coefficients on capital, which most estimators have difficulties estimating with
variables in differences, seem particularly well estimated. Columns 6 and 7, which report
the elasticities for capital and labor scaled by their sum (value added elasticities), show
that capital roughly explains from a quarter to a third of the sum. It is a remarkable sign
of robustness that all these results are obtained for the six sectors without any change in
the specification and from relatively small samples.
Column 8 reports the estimates of the elasticity of demand with respect to the own
16
price. Recall that these estimates are structural, in the sense that this is the elasticity
which characterises the function, not an estimate of the price sensitivity implicit in the
observed markup which would also depend on the particular form of market competion.
The elasticities also show sensible values, which range from a value of 7.0 to 1.6. Notice
that, under Bertrad competition, these elasticities would imply margins ranging from 14 to
62%. If these elasticities should give an idea of the degree of average product substitutability,
the results are apparently not bad: printing products and chemicals would have the highest
product differentiation, while transport equipment and metal products the lowest. Food
and textiles would occupy an intermediate position. In any case, it is important to notice
that these elasticities are only average values in broadly defined industries which are likely
to vary enormously across firms. Enlarging the specification to deal with heterogenous
intra-industry elasticities is one of the aims of our next steps in research.
The effects estimated for the shifters are quite sensible too. The variable market dynamism works as a nice indicator of shifts in demand, always positive, sizeable and picked
up with high precision. This variable may seem a little uninteresting from the point of view
of policy consequences but, given its role, one wonders how important the generated biases
are when omitted from the specification of simple production function estimates. The rate
of growth of advertising shows positive significant effects in all sectors except industry 6, in
which it is negative and non-significant. This points out an important role for advertising
as a shifter in most of the sectors. It would, however, be interesting to test for a possible
endogeneity coming from correlation in advertising changes and anticipated shocks in demand. The insignificant effect of industry 6 also indicates that possible changes through
markup effects should be checked (see the discussion on product innovation below).
The effects of innovation should be read as the average impact of the introduction of
process and product innovations, respectively. Process innovations are specified as costdecreasing shifters and hence their impact must be taken as the proportional decrease in
cost implied on average by a process innovation. Product innovations are specified as
demand shifters and hence their impact must be taken as the average increase in the firm
demand implied by the introduction of a product innovation. Coefficients are again sensible
17
and their values, interesting in themselves, are the basis for the welfare calculations. Let’s
first discuss the values of the estimates.
Process innovations always appear to decrease cost. It is true that the effects are in many
cases imprecisely estimated but we expect to improve this with the second-step estimates.
Reduction in cost typically seems to be located between 0.5 and 2.5 percentage points of
marginal cost The industries with the most important cost reducing process innovations
are 3 (Chemicals products) and 8 (Textile, leather and shoes). Product innovation appears
to raise demand in four industries. The amount can be understood as the percentage change
in quantity that the firm can sell at a given price. The average demand increases because of
the introduction of a product innovation range from 3 to almost 10%. The lowest positive
increase takes place in industry 3 (Transport equipment) and the highest in industry 1
(Metals and metal products).
The apparently puzzling question is that product innovation appears to decrease demand
in the remaining two industries: industry 3 (Chemical products) and industry 8 (Textile,
leather and shoes). In the first case, reduction is by 4 percentage points and is statistically
significant. In the second, it is by 2 percentage points and it is imprecisely estimated.
How can this be explained? The answer is related to the specification of margins. With
margins invariant with respect to innovation, the effect should be positive. But with margins
positively related to product innovation, the sign of the total demand effect can be negative
(see section 2.4). Intuitively, there are two different demand effects: one is the enlargement
of demanded quantity because the product has improved; the other is the reduction in
demand because product innovation has led to a margin enlargement and hence to a price
increase. If the second effect dominates, the total product innovation effect on demand can
be negative. Both effects can be separately identified by estimating the system consisting
of the production function and the price equation. Once the margin effect is accounted for
(see below), the impact of product innovation seems to be non-significant in the case of
industry 3 and positive and important (12 percentage points) in industry 8.
Let us present some preliminary estimates of the system consisting of the production
function and the pricing equation.Table 2 presents the results corresponding to sectors 1,
18
3 and 8. The equation for prices adds the possibility of a separate modelling of margin
but also presumably a different disturbance. In the first trials, the three reported industries
gave more or less sensible results without the need to change anything. However, the results
of the other three industries show some signs of lack of identification. A more systematic
exploration of this equation is needed. In any case, it is interesting enough that this system
works well in the two cases in which the previous system detects varying margins. The
specification also reveals significant margin effects just in these two cases. Curiously, margin
effects are negative for advertising (advertising would be associated in these two sectors to
price reductions).
In Table 3, we employ the cost-reducing and quantity-enlarging estimated effects, together
with the elasticity of demand, to estimate welfare effects. Welfare effects are for the moment
computed under the assumption of constant margins, and hence only applied to the cases
in which we presume that this assumption holds. Formulas, shown in the table, also assume
Bertrand pricing. They can be easily deduced by considering the corresponding cost and
demand displacements from one period to another, and linearly approximating the changes
in demand in the neighborhood of equilibrium. Variations in consumer surplus and profits
are given in proportion to current sales before the introduction of the innovation. The
numbers reflect static gains, or gains in the period in which the innovations are introduced.
Numbers are perfectly reasonable and show many interesting characteristics. Process
innovations imply an average welfare gain of 1.6 percentage points of sales, with two-thirds
of this gain being consumer surplus increment and the remaining third the increase in
profits. The gains due to product innovations are higher (4 percentage points) but evenly
split between consumer surplus and profits.
5. Conclusion.
This paper has carried out an exploration of the use of semi-reduced forms to estimate
the parameters of microeconomic production functions. These reduced forms employ information on the demand relationship and the pricing of firms. Estimates use a rich data
19
set which includes the firm-level changes in the price of the output and in the prices paid
by the inputs, the introduction of process and product innovations and information on two
more demand shifters: the advertising of the firm and market dynamism. Estimates have
been carried out by means of joint non-linear GMM estimation of the output and cost/price
equations. Results are very good and many implications remain to be exploited.
The main results up to here are as follows. The reduced form for output provides good
estimates for the coefficient on capital but prices have to be instrumented with variables
close to shadow price changes. On the contrary, the reduced form for average cost produces
sensible estimates for the coefficient on prices. The joint estimation of both equations,
using a minimum of instruments (shadow prices indicators and user cost of capital), gives
highly sensible results. The coefficients on capital are reasonable, returns to scale close to
one, and the elasticity of demand with respect to price takes sensible values. The estimates
for the effects of demand shifters are equally good and show positive roles in demand
enlargement for the market dynamism indicator and variations in advertising. Innovation
has an important role: process innovations reduce marginal costs, and product innovations
enlarge demanded quantities and, in some cases, are associated to margin changes.
The cost-reducing and quantity-enlarging effects, together with the elasticity of demand,
are employed to estimate current period welfare effects of innovation under the assumption of constant margins and Bertrand competition. Process innovations imply an average
welfare gain of 1.6 percentage points of sales and two-thirds of this gain is consumer surplus increment. The gains due to product innovations are higher (4 percentage points) but
evenly split between consumer surplus and profits.
20
Data Appendix:
All employed variables come from the information furnished by firms to the ESEE (Encuesta Sobre Estrategias Empresariales) survey, a firm-level panel survey of Spanish manufacturing starting in 1990 and sponsored by the Ministry of Industry. The unit surveyed is
the firm, not the plant or establishment, and some closely related firms answer as a group.
At the beginning of this survey, firms with fewer than 200 workers were sampled randomly
by industry and size strata, retaining 5%, while firms with more than 200 workers were all
requested to participate, and the positive answers represented a more or less self-selected
60%. To preserve representation, samples of newly created firms were added to the initial
sample every subsequent year. At the same time, there are exits from the sample, coming
from both death and attrition. The two motives can be distinguished and attrition was
maintained to sensible limits. Composition in terms of time observations of the whole unbalanced panel sample employed here is shown in Table A.1. Table A.2 provides descriptive
statistics and Table A.3 details the industry breakdown, from which the main estimates use
industries 1,3,6, 7,8 and 10.
Definition of variables
Advertising: Firm’s advertising expenditure deflated by the consumer price index.
Averagecost: Firm’s total costs divided by output.
Capital : Capital at current replacement values is computed recursively from an initial
estimate and the data on current firms’ investments in equipment goods (but not buildings
or financial assets), actualised by means of a price index of capital goods, and using sectoral
estimates of the rates of depreciation. Real capital is then obtained by deflating the current
replacement values.
Hours per worker: Normal hours of work plus overtime minus lost hours per worker.
Industry dummies: Eighteen industry dummies.
Industry price decrease: Dummy variable that takes the value 1 when the firm reports
an own-price decrease which has been motivated by a reduction of prices of competitors in
21
its main market.
Industry prices: Industry indices computed for 114 sectors and assigned to the firms
according to their main activity.
Labour : Number of workers multiplied by hours per worker.
Market dynamism: Weighted index of the market dynamism reported by the firm for the
markets in which it operates. The index can take the values 0d0.5 (slump), 0.5d1
(expansion) and d=0.5 (stable markets). Included in regressions in differences from 0.5.
Materials: Intermediate consumption deflated by the price of materials.
Output: Goods and services production. Sales plus the variation of inventories deflated
by the firm’s output price index.
Price of materials: Paasche-type price index computed starting from the percentage
variations in the prices of purchased materials, energy and services reported by the firms.
Divided by the consumer price index except when used as a deflator.
Price of the output: Paasche type price index computed starting from the percentage
price changes that the firm reports to have made in the markets in which it operates.
Product innovation: Dummy variable that takes the value 1 when the firm reports the
accomplishment of product innovations.
Process innovation: Dummy variable that takes the value 1 when the firm reports the
introduction of a process innovation in its productive process.
Utilisation of capacity: Yearly average rate of capacity utilisation reported by the firm.
User cost of capital : Weighted sum of the cost of the firm values for two types of long-term
debt ( long-term debt with banks and other long-term debt), plus a common depreciation
rate of 0.15 and minus the rate of growth of the consumer price index.
Wage: Firm’s hourly wage rate (total labour cost divided by effective total hours of
work). Divided by the consumer price index.
22
Appendix
In this appendix we briefly comment on some previous estimates for the whole sample.
Table B1 reports the main results of the direct conventional production function estimates. Capital and utilisation of capacity always tend to obtain close coefficients (a bit
lower for capital) and we opt for reporting the results for the constrained variable (variation in) “used capital.” OLS results are not bad. Capital attracts a statistically significant
coefficient, although somewhat small: 19% of the sum of the capital and labour elasticities
(see Value added elasticities). Returns to scale, as is usual in OLS estimates, turn out to
be diminishing (elasticity of scale is less than 0.8). The use of different ways of deflating
the output measure has a small impact on the estimates. It is worthy of noting that the
main impact is not on the elasticity estimates, but on the constant and the innovation effect
estimates.
IV estimation is carried out with conventional instruments. Labour and materials are
instrumented, in a GMM framework, with their levels lagged two periods at each crosssection. The number of lags used can be increased without important changes. The variable
capital plus utilisation of capacity is instrumented using the capital growth rate at t-1.
Notice that this is a valid instrument under the assumption that capital is a predetermined
variable, which can also be considered to take utilisation of capacity as endogenous. The
Sargan test of overidentifying restrictions points to the validity of the instruments. The
IV estimation increases all coefficients, but the coefficient on materials and the coefficient
on capital quite a bit more. Precision, however, is low. Returns to scale now tend to be
increasing (elasticity of scale is 1.08 at the estimate which uses individual prices). The
estimate which uses individual prices now seems to be more sensible, mainly providing a
better account of the impact of innovation.
We conclude that conventional estimators in differences seem to give estimates that are
not bad when used with enough quality data and slightly better estimates if firm-level prices
are available. However, neither the OLS estimates nor the IV estimates are fully convincing.
The IV estimate is probably the closest to reliable values, but quite imprecise.
23
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25
Industry
No. of
firms
εK
Table 1
Estimating the parameters of the production and cost functions
Joint nonlinear GMM estimates1,2
Value added
Price
Elasticities
Returns
elasticities
elasticity
εL
εM
to scale
K
L
η
Process
innovation
Shifters
Product
innovation Advertising
Market
dynamism
1. Metals and metal products
168
0.079
(0.021)
0.235
(0.041)
0.627
(0.070)
0.941
(0.049)
0.252
(0.075)
0.748
(0.075)
6.959
(2.454)
0.003
(0.005)
0.096
(0.036)
0.029
(0.016)
0.214
(0.071)
3. Chemical products
173
0.073
(0.020)
0.147
(0.033)
0.680
(0.057)
0.900
(0.062)
0.331
(0.117)
0.669
(0.117)
2.365
(0.527)
0.023
(0.006)
-0.041
(0.016)
0.043
(0.012)
0.106
(0.030)
6. Transport equipment
88
0.076
(0.019)
0.235
(0.044)
0.645
(0.077)
0.956
(0.065)
0.244
(0.079)
0.756
(0.079)
6.469
(1.315)
0.006
(0.007)
0.028
(0.028)
-0.017
(0.015)
0.100
(0.047)
7. Food, drink and tobacco
234
0.043
(0.013)
0.086
(0.028)
0.702
(0.051)
0.832
(0.072)
0.335
(0.185)
0.665
(0.185)
3.744
(1.073)
0.007
(0.005)
0.085
(0.021)
0.024
(0.013)
0.188
(0.039)
8. Textile, leather and shoes
214
0.058
(0.028)
0.186
(0.031)
0.625
(0.067)
0.869
(0.066)
0.238
(0.124)
0.762
(0.124)
3.084
(1.114)
0.015
(0.006)
-0.022
(0.023)
0.055
(0.016)
0.166
(0.035)
10. Paper and printing products
101
0.093
(0.029)
0.167
(0.047)
0.494
(0.059)
0.754
(0.111)
0.359
(0.160)
0.641
(0.160)
1.571
(0.423)
0.007
(0.008)
0.064
(0.022)
0.013
(0.009)
0.098
(0.026)
1
First-step standard errors in parentheses, robust to arbitrary autocorrelation over time and heteroskedasticity across firms.
Orthogonality conditions for both equations: innovation dummies (process and product), advertising, market dynamism, utilization of capacity, lagged user cost of capital (own and rivals).
Orthogonality conditions for equation on output: hours of work, rival’s price decrease; Orthogonality equations for equation on cost: wage, price of materials.
2
Table 2
Estimating the parameters of the production function and price equation
Joint nonlinear GMM estimates1,2
Value added
Price
Elasticities
Returns
elasticities
elasticity
Process
εL
εM
to scale
K
L
η
innovation
Shifters
Product
innovation3 Advertising3
Industry
No. of
firms
1. Metals and metal products
168
0.072
(0.016)
0.191
(0.028)
0.635
(0.054)
0.898
(0.052)
0.273
(0.083)
0.727
(0.083)
12.199
(3.691)
0.004
(0.004)
0.129
(0.054)
-0.002
(0.005)
0.003
(0.017)
-0.004
(0.003)
0.377
(0.090)
3. Chemical products
173
0.074
(0.016)
0.076
(0.016)
0.627
(0.048)
0.777
(0.062)
0.493
(0.184)
0.507
(0.184)
3.306
(0.657)
0.024
(0.005)
-0.013
(0.015)
0.017
(0.008)
0.022
(0.008)
-0.012
(0.005)
0.177
(0.032)
8. Textile, leather and shoes
214
0.038
(0.015)
0.127
(0.025)
0.616
(0.050)
0.782
(0.078)
0.230
(0.135)
0.770
(0.135)
13.886
(3.726)
0.011
(0.005)
0.121
(0.058)
0.016
(0.007)
0.042
(0.021)
-0.012
(0.004)
0.566
(0.125)
1
εK
Market
dynamism
First-step standard errors in parentheses, robust to arbitrary autocorrelation over time and heteroskedasticity across firms.
Orthogonality conditions for both equations: innovation dummies (process and product), advertising, market dynamism, utilization of capacity, lagged user cost of capital (own and rivals).
Orthogonality conditions for equation on output: hours of work, rival’s price decrease; Orthogonality equations for equation on cost: wage, price of materials.
3
First-line coefficients are effects on demand, the second line effects on margin
2
Table 3
Welfare effects of innovation (in proportion of current sales)1,2
Process innovation
Product innovation
∆cons. surplus
∆firm profits
∆total
∆cons.r
surplus
h
i ∆firm profits
η−1 c−c0
c−c0
1
c−c0 2
c−c0 2
1 q0−q 2
1 q0−q
1 q0−q
+
η(
)
(
)
−
(
)
+
(
)
c
2
c
η
c
c
η
q
2
q
2( q )
1. Metals and metal products
3. Chemical products
6. Transport equipment
7. Food, drink and tobacco
8. Textile, leather and shoes
10. Paper and printing products
1
2
0.003
0.024
0.006
0.007
0.015
0.007
0.003
0.013
0.005
0.005
0.010
0.002
0.006
0.036
0.011
0.012
0.025
0.010
0.014
0.004
0.024
0.042
Computed with the effects reported in Table 1. Product innovation effects are not computed for sectors 3 and 8.
q0−q
( c−c0
c ) = proportional change in marginal cost, ( q ) = proportional change in output, η = elasticity of demand
0.014
0.004
0.023
0.041
∆total
0.028
0.009
0.046
0.083
Table A1. Sample detail
No of years
in sample
3
4
5
6
7
8
9
10
Total
No of firms
230
215
204
150
115
143
142
209
1408
Observations
690
860
1020
900
805
1144
1278
2090
8787
Table A2. Variable descriptive statistics
Mean
St. dev
Min
Max
Dependent Variables
Output
Average cost
0.031
0.021
0.239
0.154
-2.6
-1.2
2.4
1.1
Explanatory Variables
Advertising
Capital
Hours per worker
Industry price decrease
Industry prices
Labour
Market dynamism
Materials
Price of materials
Price of the output
Process innovation
Product innovation
User cost of capital
Utilization of capacity
Wage
0.023
0.081
-0.001
0.058
0.022
-0.008
0.504
0.021
0.035
0.014
0.332
0.266
0.135
0.001
0.054
0.903
0.313
0.065
0.234
0.034
0.190
0.320
0.350
0.060
0.056
0.472
0.442
0.046
0.191
0.190
-2.0
-2.1
-1.7
0
-0.21
-2.8
0
-3.3
-0.5
-0.7
0
0
0.1
-2.3
-1.5
2.0
7.3
1.7
1
0.4
1.7
1
5.4
0.7
0.7
1
1
0.4
2.9
2.4
Industry dummies
Ferrous and non-ferrous metals
Non-metallic mineral products
Chemical products
Metal products
Agricultural and ind. machinery
Office and data processing machin.
Electrical goods
Motor vehicles
Other transport equipment
Meats, meat preparation
Food products and tobacco
Beverages
Textiles and clothing
Leather, leather and skin goods
Timber, wood products
Paper and printing products
Rubber and plastic products
Other manufacturing products
0.022
0.075
0.071
0.098
0.053
0.009
0.076
0.045
0.020
0.031
0.117
0.021
0.116
0.032
0.065
0.073
0.053
0.025
0.146
0.263
0.256
0.298
0.225
0.093
0.264
0.207
0.138
0.174
0.321
0.143
0.321
0.176
0.246
0.260
0.224
0.155
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Table A3. Industry definitions and equivalences
1
Industry breakdown
Ferrous and non-ferrous
metals and metal products
1+4
ESEE clasiffication
Ferrous and non-ferrous metals +
Metal products
2
Non-metallic minerals
2
Non-metallic minerals
3
Chemical products
3+17
Chemical products +
Rubber and plastic products
4
Agricultural and ind. machinery
5
Agricultural and ind. machinery
5
Office and data-processing
machines and electrical goods
6+7
Office and data processing machin. +
Electrical goods
6
Transport equipment
8+9
Motor vehicles +
Other transport equipment
7
Food, drink and tobacco
10+11+12
Meats, meat preparation +
Food products and tobacco + Beverages
8
Textile, leather and shoes
13+14
Textiles and clothing +
Leather, leather and skin goods
9
Timber and furniture
15
Timber, wooden products
10
Paper and printing products
16
Paper and printing products
Table B1 Conventional production function estimates1
2
Dependent variable: Output
Sample period: 1992-1999
Method of estimation3
Independent variables
Constant
Process innovation dummy
Capital+Utilization of capacity
Labour
Materials
Time dummies
Industry dummies
OLS
0.015
0.016
0.066
0.277
0.429
(0.002)
(0.004)
(0.012)
(0.027)
(0.022)
included
OLS
0.008 (0.002)
0.012 (0.003)
0.069 (0.011)
0.289 (0.026)
0.43 (0.022)
included
IV
0.006
0.013
0.177
0.327
0.577
(0.009)
(0.004)
(0.124)
(0.167)
(0.078)
included
IV
-0.003 (0.010)
0.007 (0.004)
0.210 (0.128)
0.328 (0.174)
0.593 (0.080)
included
Statistics
Instruments
Capital growth rate at t-1
Labour and materials
t-2 lagged levels at each cross-section
Sigma
Residuals’ first-order correlation4
Residuals’ second-order correlation4
Sargan test (degrees of freedom)
0.108
(-8.4)
(-1.6)
0.107
(-8.5)
(-2.0)
0.120
(-7.7)
(-0.3)
15.5 (14)
0.121
(-8.0)
(-0.3)
17.2 (14)
No. of firms
No. of observations
1,408
5,971
1,408
5,971
1,408
5,971
1,408
5,971
Returns to scale
0.772
0.788
1.081
1.131
0.191
0.809
0.193
0.807
0.351
0.649
0.390
0.610
Elasticities
Value added elasticities:
Capital
Labor
1
All non-dummy variables in (log) growth rates.
First and third columns deflated by individual prices, second and fourth columns deflated by industry prices.
3
Robust standard errors in parentheses.
4
Arellano-Bond test value.
2